Barrier crossing in the presence of multi-exponential memory functions with unequal friction amplitudes and memory times

Abstract

We study the non-Markovian Langevin dynamics of a massive particle in a onedimensional double-well potential in the presence of multi-exponential memory by simulations. We consider memory functions as the sum of two or three exponentials with different friction amplitudes γi and different memory times τi and confirm the validity of a previously suggested heuristic formula for the mean first-passage time τMF P . Based on the heuristic formula, we derive a general scaling diagram that features a Markovian regime for short memory times, an asymptotic long-memory-time regime where barrier crossing is slowed down and τMF P grows quadratically with the memory time, and a non-Markovian intermediate regime where barrier crossing is slightly accelerated or slightly slowed down, depending primarily on the particle mass. The relative weight of different exponential memory contributions is described by the scaling variable γi/τ 2 i , i.e., memory contributions with long memory times or small amplitudes are negligible compared to other memory contributions.

Non-Markovian modeling of protein folding

“…In fact, the values of and go down as moves to the respective start positions (i.e., as the folding and unfolding times become shorter). This reflects that memory effects particularly accelerate fast transitions ( 36 – 38 ).…”

“…1 , one obtains ns, which is of the order of the longest memory time . This places the system in the so-called memory-acceleration regime, where memory effects are relevant and significantly accelerate barrier crossing ( 36 – 38 ).…”

“…This stays true even when the friction coefficient is allowed to depend on the reaction coordinate. As predicted by the Grote–Hynes theory, memory typically accelerates barrier crossing, where the acceleration magnitude depends primarily on the ratio of the memory time and the distance between the minimum and the barrier in reaction coordinate space ( 33 – 38 ). This memory-induced speedup of folding and unfolding is found to be accompanied by pronounced anomalous diffusion in reaction coordinate space.…”

Barrier crossing in a viscoelastic bath

“…during chemical reactions [1][2][3], protein folding [4][5][6][7][8], nanomagnetic domain reversal [9], or even drug absorption [10]. As an important extension of the Kramers' problem, several studies considered a non-Markovian bath where memory effects influence the barrier crossing dynamics [11][12][13][14][15][16][17][18][19][20][21]. Such fluids are often found in biological environments but are also widespread in technical systems.…”

Fluid viscoelasticity triggers fast transitions of a Brownian particle in a double well optical potential

“…Their motion is commonly described by the generalized Langevin equation [40] with nonequilibrium transient effects that markedly manifest themselves in presence of driving forces [41][42][43][44][45]. Although generalizations of Kramers rate theory to systems with longmemory friction have been developed in the past [46][47][48][49], apart from a few numerical works [28,29,[50][51][52], their predictions remain largely unexplored in experiments.…”